MIT-SCIENCE-Lectures-syl2003
MIT-SCIENCE-Lectures-lec03 (2)
Lecture Notes - 37.24/7.88J/5.48JThe Protein Folding Problem• Reprise RNase refolding• General Features of Globular proteins• Interior PackingRnase RefoldingWe can cartoon the experiments:Assume that reduced form is unfolded and populates an ensemble of unfolded states in 8M urea:[U]Rapidly exchanging statistical ensemble of random coils[I]???[N]Native fold, $ S-S bonds, 1 out of 105 possible sets of S-S bonds [Aggregated]Non-native (no enzymatic activity), non-native (scrambled) disulfide bonds.At the end of the reaction we have native stateSoluble inactive – misfolded or perhaps small oligomersPrecipitated: Anfinsen showed that these were S-S bonded network = he called “scrambled”Critical question is nature of the intermediates as go from here to there:If there was a sequence in which these bonds formed, and one could figure out the sequence or pathway, it might give you considerable information on the steps in the folding pathway.So certainly we need to understand native-fold, and interactions that determine it, stabilize it once formed;However this does not solve problemWe will return to the question after reviewing the general anatomy of globular proteins, which will occupy most of next week.General features of 3-D structures of solved proteins; Globular, Soluble proteins:A. Isolation and CrystallizationThe first crystals of proteins sufficiently large and ordered to diffract X-rays were prepared of the digestive enzyme pepsin:Bernal, J.D., and Dorothy Crowfoot. Nature (1934): 133, 794.This was followed by crystals of insulin, Lactalbumin, hemoglobin, andchymotrypsin:Bernal, Fankuchen, and Perutz (1938)The rise to power of the Nazis in Germany and Italy and the outbreak ofwar brought all these studies to a halt. Bernal led the world scientificcommunity into opposition to the fascists. This was not only with respect to the their persecution of Jewish scientists, but that the notion of Aryanscience different from the general growth of knowledge, represented abroader attack and the growth and communication of knowledge.The rebuilding and repopulating of the civilian biomedical infrastructuretook about ten years, and re-launched in the 1950’s. In England - BritishMedical Research Council, in US - National Institutes of Health.Solution of Myoglobin structure by John Kendrew in 1958 and hemoglobin structure in 1962 by Max Perutz - it became clear that alpha helix actually present in globular proteins. With the solution of the lysozyme structure by David Phillips (1966), revealed that anti-parallel beta-pleated sheet alsopresent in globular proteins.B. Review Criteria (Biases) for the selection of proteins forcrystallization and perhaps into the success or failure ofcrystallization1. Available in large quantities - usually extracellular protein fromextracellular fluids• Hemoglobin from blood• Myoglobin from muscle• Lysozyme from egg white/ tears??• Ribonuclease from stomach??• Insulin from pancreas??• Lactalbumin from milk ??• Chymotrypsin; from saliva, stomach??2. Stable during purification• Resistant to Residual proteases• Does not aggregate• Resistant to Cold denaturation3. Very soluble in aqueous buffersThis excludes:• Fibrous proteins; evolved to interact with each otherto form structures; keratin, collagen• Other Structural proteins; ribosome structuralproteins, histones, actins, tubulins• Membrane proteins4. Must crystallize• Proteins which behave differently than the dogma;take multiple conformations in solutionProtein database sharply under-represents – fibrous proteins, structural proteins, membrane proteinsC. Structures whose atoms have been located at high resolution- Globular aqueous soluble: 1,100 domains(- Membrane: 12)(- Fibrous: 5)This is the class of proteins for which single crystals have been obtained.Clearly the most extensive database is for proteins soluble in aqueoussolutions and which form crystals.D. General Features of Crystallized Globular Proteins1. Surface/Volume RelationshipsGlobular proteins have relatively sharply defined:• Exterior Surface = H20 Interface• Interior volume - Is the interior of a native proteincrystalline or oily?A quantitative answer to this was given by Richards:"The Interpretation of Protein Structures: Total Volumes, Group Volumes and Packing Density" Frederic M. Richards (1974) J. Mol. Biol., 82, 1 - 14.Problem comes down to calculating how densely packed atoms are inprotein molecules?We can define the packing density of a molecule as:Volume of its van der Waals envelopes of its constituent atoms / actual volume of the intact folded moleculeThis value is dimensionless- Close packed hard spheres = 0.74- Close packed infinitely long cylinders = 0.91- Crystals of various small organic molecules 0.70 - 0.78 values (<0.6very rare)The van der Waals radii - from interatomic distances of nonbondedatoms in organic crystals.However calculation of the volume of irregular structures not trivial.Richards’ procedure made use of a geometrical construct calledVoronoi polyhedra.• Draw vector from each atom to closest surroundingatoms.• Draw a plane through it corresponding to intersectionof van der waals radii. This will define a polygon.• When you do this for all atoms space is completelyfilled.• Thus obtain geometrically legitimate volume. Cancompute this from atomic coordinates.For the following solved proteins, the average packing density:• Hen egg white lysozyme = 0.75• Ribonuclease S = 0.74Conclusion: The interior of globular proteins is as tightly packed as areamino acids in organic crystals.Subsequent investigations have supported this general result for thatset of proteins included in crystallized set.Counter argument; rigidity necessary for crystallization is only found inthose proteins which are continuously dense and lack hinges.2. Are there interior cavities or entrained solvent bobs?Careful examination of a larger set of proteins was carried out byA.A. Rashin, Michael Iofin, and Barry Honig (1986) "Internal Cavities and BuriedWaters in Globular Proteins" Biochemistry, 25, 3619-3625.These procedures involve in general:• Construction of Van der Waals radii;• Find places where these radii not buried or in contact with other radii;• Use a spherical probe (water model = sphere radius 1.4A) walkalong van der Waals radii with smaller and smaller probe to findplaces that can walk alongAccessible surface area is defined by center of water molecule rollingover van der Waals surface. Thus there exists inaccessible surface area.Gives an estimate of volume of cavity and accessible surface area.H2Os# Protein MW#VolA3Pancreatic Trypsin Inhibitor 6,000 2 70 4cytochrome c 11,000 5 34 24115ribonuclease 13,000egg lysozyme 14,000 8 190 54019erythrocruorin 14,0001391Myoglobin 17,0002317494trypsin 23,00013chymotrypsin 26,000 26 571 10• Cavities = less than 2% of the volumes of theseproteins.• No single cavity can host a probe of 2A or more.• Almost all cavities become connected to proteinsurface as probe diameter goes down to 0.4 A.What does this suggest?Suggests that these represent channels or hinges.Volume of internal water molecule for larger cavities is about 30AVan der waals radius of water is about 1.4 ASome cavities which appear non-polar can contain a water moleculeforming three hydrogen bonds. This is because the hydrogen bond canbe longer than the sum of the van der waals radius of a polar atom anda probe., and thus some polar atoms with which water forms hydrogenbonds may not contribute to the accessible surface.Note: those cavities that seem to be empty could be contributing boundwater, but if water crystallographically not fixed, smeared out.3. Functional Significance of small cavitiesLargest empty cavity in their sample located between helices B, E, andG, between two domains of the globin.Conserved in six other myoglobin type proteins (Very diverse). May beimportant for relative motions of helices.More than half of cavities in multi-domain proteins are at domaininterfaces.He considers similar, linkage explanation, rather than packing problem.Prediction; Those sequences that have evolved can close pack?Question: WHAT FRACTION OF amino acid sequences is there noclose packed globular structure?For retinal containing pigments models suggest that cavity of 100Awould allow for rotation of chromophore.Further studies carried out by:"Interior and Surface of Monomeric Proteins" Susan Miller, Joel Janin Arthur Lesk and Cyrus Chothia (1987) J. Mol. Biol., 196, 641-656.For example lysines and arginines almost always at surface (<4%buried)4. Additional Features of Inside OutsideGeneral Features of Globular proteins• No Knots• More than half of the polypeptide sequence isorganized into regular secondary structure,predominantly alpha helices and beta sheets• Interiors are densely packed - Extremely rare to burybulk solvent• Buried charges very rareo In rare cases, ion pair, metal complex, oractive site• Interiors are hydrophobic (carbonyls and amides areH-bonded)• A large fraction of the accessible surface of theextended polypeptide chain is buried in the proteininterior.E. Conclusions re protein folding1) Buried side chains truly removed from water: Major energetic contribution toprotein folding; but driving force, as originally proposed by Walter Kauzmann, is entropic effect on water structure; hydrophobic residues cannot H bondwith water; organizes water molecules with respect to own partners.2) These side chains almost always hydrophobic: extremely rare to burycharged side chains; If the inside of a protein is closely packed and excludes water, becomes quite clear that in fact the inside and the outside are verydifferent environments. Therefore the partitioning of residues into the chainbetween interior and surface positions may be very important in defining fold.3) Contradiction: Burying side chains also requires burying backbone; butbackbone has Carbonyl oxygens and amide nitrogens which are hydrophilic, polar groups;4) But in actual fact, largest number of peptide bonds in proteins are partof regular secondary structures, alpha helices and beta sheets: partialcharges are neutralized by maximal hydorgen bond formation:5) SO naively folding processes may have at least two level of organizationFormation of secondary structure, docking against each other to formtertiary structure; Framework model:Now clearly, given the large fraction of chain that is in regular secondarystructure, a substantial fraction of the internal packing of globular proteins is the...So at least two processes that we need to investigate:• Formation of secondary structure;• Next level; packing of secondary structure into tertiary structure: Might be tightly coupled;F. Packing of Secondary StrcuturesOne of the determinants of the shapes of proteins and the folds is thepacking of the units of secondary structure against each other.Short amino acid sequences = peptides > At room temperature in constantmotion; flickering in and out between a variety of conformations;Homopolymers; In solution also flickering in and out between non-regularconformations and mixture of these with alpha helices;Two levels of Packing:• Within units of secondary structure; alpha helix, beta strands• Between units of secondary structure- helix/helix, helix /sheet• Packing Interactions critical for formation of native structure.。
MIT-SCIENCE-Lectures-essay1(1)
21L703 Renaissance Drama Fall 2003Prof. Shankar RamanEssay Assignment 1: Due : Sep 29 by 5pm(leave papers in envelope attached to my office door, or in mailbox)Length : 5-6pages, double spaced throughout, standard 12 pt font such as Times, one inch margins.I assume that you have read Hamlet and The Spanish Tragedy thoroughly in order to prepare for class discussions and paper. Before you write:This assignment is intended to get you used to reading the text closely, anddeveloping an argument through close reading. Skim again through either Hamlet or The Spanish Tragedy , noting those passages or parts of scenes that most attract your attention. Thinking about these, try to articulate a question or a problem that your paper willaddress. Use the question to figure which sections of the chosen text need to be addressed in your essay. Then, outline your paper, trying to break it down into its conceptual ‘moves,’ and deciding what sorts of textual evidence are required for each ‘move.’ Writing the essay:Now, you are in the position to begin your essay. Please compose a 5-6 pageessay in which you develop a clear and focused argument that addresses the central question or problem you have identified. Be specific and focused, citing the text to develop and support your claims. The task is not to go through passages line by line, listing everything you have noticed. Rather, concentrate on what you consider to be the most important aspects of a chosen passage in relation to the theme of your essay. You will thereby be ranging over the play as a whole, making connections that have at their centre the issues raised by the passage you have chosen. You should organise yourassertions and observations in such a way that they contribute to a single important claim you want make about the play.It is not sufficient to say, for instance, that a specific passage "heightens" or"augments" something the play is interested in. That is a vague thesis that simply prompts the question: so what? You need to have a focussed claim that examines the significance of the issues raised by the play and thinks in specific terms about how the passages you have chosen contributes to the elaboration of those issues. Try to move beyond character analysis to make the link between individual moments or actions and the larger issues with which the play deals. After you write:After you have written the paper, re-read and edit it to make sure that you have eliminated typographical and grammatical errors. Examine the transitions betweensentence and paragraphs and re-work the paper so that it flows smoothly from beginning to end. To cite from the play follow the convention: 1/ the first time you cite, include a footnote detailing the edition you are using 2/ thereafter, simply include citation in parentheses in the body of the text, e.g., (2.3.32-39).Finally, remember the injunction against plagiarism. If you borrow ideas from elsewhere, or use language from other sources, you are expected to acknowledge explicitly in footnotes or bibliography the nature of your reliance. Such acknowledgement needs to be made not just for direct quotation, but for paraphrasing the ideas of an external source as well.Some questions to get you started (entirely optional---feel free to choose any topic you like):What is the relationship between earlier and later versions of the ST? That is, how do the additions work (or not) in relation to the text we studied?Frames and plays-within-plays: both ST and H make good use of these. Contrast the function and development of such motifs in the two plays (or, choose one of the plays, and discuss its use of frames, internal dramas and other such indicators of meta-theatricality).How does Hieronimo’s alteration or transformation by vengeance affect your reading of Hamlet (the character)?Would Hamlet be possible without The Spanish Tragedy? (a wide-ranging topic, with many possible specific angles).Discuss the relationship between the dyanamics of the family and the corruption of state in the plays.What do we make of Polonius and Hieronimo as the heads of functionary families, both of whom suffer unjust victimisation?The use of figures of speech, rhetorical devices and tropes in the two playsThink about soliloquies and their functions in the plays: who gets them? How do they work? What sorts of relationships between audience and play do they establish?Use of letters and second-hand narration in both plays.Use of props in the two playsThe use of minor characters in the two plays.。
MIT-SCIENCE-Lectures-intro_sts_p12003
INTRODUCTION TO STATISTICS FOR POLITICAL SCIENCE:1.IntroductionStephen AnsolabehereDepartment of Political ScienceMassachusetts Institute of TechnologyFall,20031.IntroductionStatistical tools are essential for social scientists.Basic concepts of statistics,especially randomness and averaging,provide the foundations for measuring concepts,designing stud-ies,estimating quantities of interest,and testing theories and conjectures.People are not always good statisticians.It is hard to maintain discipline in observing the world.W e often learn from what is convenient-a violation of random sampling.We often do not calculate averages well.To learn these concepts with the depth associated with a graduate education-where you will have the facility to use these concepts in your own research and possibly contribute to the development of statistical models that others may use-requires some mathematics.We will use,repeatedly,three sorts of functions-polynomials(especially quadratics),exponentials, and logarithms.We will also use summation,as that is necessary for the calculation of averages,and summation comes in two forms-discrete and continuous(or integration).We will use di®erencing and di®erentiation(the continuous version of di®erencing).Finally,we will use probability a special branch of mathematics designed to study uncertainty.This course is designed to be a self-contained introduction not only to the concepts but also to the tools of statistics for social sciences.At the beginning of this course I will review the basic mathematical tools used in statistics.As a result we will study calculus and probability theory.Much of the basic mathematics that social scientists use in statistical analyses and in formal modeling comes from the calculus,especially limits,derivatives,and integrals.Probability provides a theory of uncertainty,and is thus the essential tool of statistics.1.Two core ideas in statistics.A.AveragingStatistics involves studying the frequencies of events and behaviors.W e assume that every event has its own likelihood of occurence,such as the likelihoodof the birth of a boy or girl.The long-run average is a measure of that frequency.One important law of statistics is the Law of Large Numbers.If we observe the repetition of a certain trial or experiment or event,such as birth,the long-run frequency with which one outcome or another happens,such as a boy or a girl is born,is extremely close to the true frequency of that outcome.A second important law of statistics is the Central Limit Theorem,which states that the frequency of possible outcomes of a sum of variables follows a bell-shaped(or normal)curve.We will make both of these laws more precise later in the course.B.RandomnessProbability is the study of randomness and chance.The systematic study of probability emerged as an important mathematical subject of study in the18th Century.In the late 18th and19th Centuries the application of probability spread beyond games of chance to the study of physical and social behavior.And in the20th Century researchers realized that one could use randomness to increase the e±ciency with which we learn.That is perhaps the most surprising and counter intuitive aspect of statistics{randomness is useful.Two core applications of this idea are(1)random sample surveys and(2)randomized experiments.1.Random Sample Surveys:How can we learn about100million people with just1000?Random sample surveys are the most widely used tool for measuring quantities of interest in all of the social sciences.Nearly all government data are collected using random sample surveys-including measures of the economic and social conditions of the nation,ranging from crime to in°ation to income and poverty to public health.Random sample surveys are staples of political organizations and academics interested in understanding national opinion about important public policies and public o±cials.How do random sample surveys work?A relatively small group of people are chosen at random and interviewed.The average answer to a particular question in a random sample istaken to represent or measure the average answer to that question in the entire population from which the sample is taken.How many people are to be interviewed and what they are to be asked is a matter of choice for the social scientist.But,the power of the random sample survey is that random choice of individuals gives the researcher leverage-allowing for great economy in the study of populations.2.Randomized ExperimentsPeople have conducted controlled experiments for centuries,especially using physical ob-jects.Controls involving creating conditions in which all other factors are held constant. Even with the best controlled experiments,it is possible to leave some potentially important factor uncontrolled.Such uncontrolled factors might create spurious relations or mask im-portant e®ects.Perhaps the most profound contribution of probability theory to scienti¯c study of social and physical behavior is the notion that random assignment of individuals to di®erent experimental conditions(such as receiving a drug or receiving a placebo)can reduce or even eliminate the threat of spurious e®ects.2.Fundamentals of Research MethodsA.Measurement and Estimation1.Concepts and Variables{the constructs or behavior we wish to understand.A good example is\inequality."Exercise:De¯ne inequality.2.Measures{the mathematical representation of the concept.For example,the income distribution in a society might be used to measure inequality.Exercise:devise a measure of the total amount of income inequality in a country.3.Measurement Theory{what requirements do we impose on our measurement device.(i)accuracy(with enough observations we would arrive at the correct answer),(ii) precision(low noise),(iii)reliability(can replicate).B.Model Building1.E®ects and Behavioral RelationshipsSocial scientists freqently want to measure the e®ect of one factor on another.There are many such examples.What is the e®ect of police on crime?What is the e®ect of additional military force on the probability of winning a battle or war?How does class size a®ect educational performance?How do electoral rules,such as single member districts,translate votes into legislative seats?In each case,there is one factor whose levels or values we would like to vary,such as the number of police,in order to observe changes in a second factors,such as the crime rate. The¯rst factor we call an independent variable,and the second factor,a dependent variable.2.AccountingWe seek to make a complete accounting of behavior.In this respect we value models in which a set of variables has high explanatory power.W e also demand parsimony:simpler is better.Example.Housing sales prices can be predicted very well as a function of list prices.In a normal market sales prices are92percent of list prices,and the¯t is extremely good.3.Equilibrium ConceptsMany ideas and conjectures about how social relations produce outcomes:maximizing behavior,dynamic adjustment,e±cient markets,or natural selection.The forces that cre-ate social outcomes make it di±cult to give causal interpretations to observed e®ects or relationships.C.InferenceA fundamental methodological problem is knowing when you should go with one argu-ment or idea or a competing argument or idea.When we measure phenomena,we often thenuse the measurements to draw inferences about di®erent ideas.Are data consistent with an argument or idea?What conclusions can we draw about theories from data?In the end, then,statistics involves a bit of decision theory.Predictions of a theory or conjectures about the world are called hypotheses.When specifying hypotheses it is important to be clear about all of the possible values.In a court of criminal law,hypotheses are questions of guilt or innocence.In medicine,hypotheses are about the condition of the patient,such as whether a cancer is benign or malignant or whether a woman is pregnant or not.In the scienti¯c method generally,the question is whether an conjecture is true or not.Unfortuantely,we never observe the truth.We use data to make decisions about hy-potheses.The evidence brought to a trial are data.A series of test are data.An academic study generates data.The problem of inference is how to use data to make decisions about hypotheses.Ultimately,that will depend on the value we place on di®erent sorts of outcomes from our decisions.However,we can formulate the problem we face quite simply.We want to make the correct decision,and we can make a correct decision one of two ways.First,we may decide,using the data,that the hypothesis is true and the state of the world is such that it is true.Second,we may decide,using the data,that the hypothesis is not true and the state of the world is such that the hypothesis is not true.W e may also make errors two ways.W e may decide that the hypothesis is true when it is in fact false or we may decided that the hypothesis is false when it is infact true.One a central objective of researchers is to avoid either of the two sorts of errors.Sta-tistical design is fundamentally about how to minimize the chances of making a mistaken judgment.。
MIT-SCIENCE-Lectures-sgquiz32003
2003 1.018/7.30J Fall Fundamentals of EcologyStudy Guide for Quiz 3As noted in the course information handout, the third exam is cumulative. However, it will focusprimarily on material from the last third of the class, beginning with Lecture 13, Population Growth.Material from the first two-thirds of the class will not be tested at the same level of specificity as onprevious tests.Assigned readings:Krebs: Chapter 28: Pages 583-590Parameters9: PopulationChapterChapter 10: Demographic Techniques: Vital StatisticsPopulationGrowth11:ChapterChapter 12: Species Interactions: CompetitionChapter 22: Pages 447-448Chapter 13: Species Interactions: PredationArticles: Gilg O. et al. 2003. Science. 302:866.et al. 2000. Nature. 405:562.TurchinP.Tilman D. 2000. Nature. 405:208.Ranta E. 2003. Science. 301:171There is a lot of information in the textbook that we did not cover in lecture. While the test is mostlikely to focus on material we discussed in class, any of the material from the assigned text is fairgame.Concepts:• Exponential growth• Carrying capacities and the logistic equation• Ecological footprint• Life tables• Survivorship curves• Resource vs. interference competition• Lotka-Volterra isoclines for competition• Tilman’s approach to competition• Gause’s and Huffaker’s experiments• Fundamental vs. realized niches• Competitive exclusion principle• Lotka-Volterra and Rosenweig-MacArthur isoclines for predation• Functional response curves• Conditions for coexistence under competitive and predator-prey interactions。
MIT-SCIENCE-Lectures-h5_24500s03
24.500 Topics in Philosophy of MindOther MindsSpring 2003/handout 5Davidson, “Three varieties of knowledge”Knowledge:A: of the contents of my own mindB: of the world around meC: of what goes on in other people’s mindsThe claim is that one can’t have one of these kinds of knowledge without having the others.An outline of the argument:1. Belief is a condition of knowledge2. In order to have beliefs, one must grasp the concept of objective truthWhat seems at least defensible is that in order to have the concept of belief, “one must grasp the concept of objective truth”. So we need an argument that having beliefs entails having the concept of belief (see “Rational animals”, 104).3. In order to have the concept of objective truth, one must communicate in a language with anotherWhat seems at least defensible is that in order to discover that some creature has the concept of truth, we need to observe the creature communicating in a language with another.Alternatively, 2 and 3 could be replaced by:2* In order to have beliefs, one must communicate in a language with another.And one might begin the argument for 2* by claiming that in order todiscover that some creature has beliefs, we need to observe the creature communicating in a language with another.4. Knowledge of other minds is a necessary condition for linguistic communication5. Knowledge of the world is a necessary condition for linguistic communication Therefore:6. If one has any knowledge at all, one has A- and B-type knowledgeWhat about C?we are not in a position to attribute thoughts to others unless we know what wethink since attributing thoughts to others is a matter of matching the verbal andother behavior of others to our own propositions or meaningful sentences.Knowledge of our own minds and knowledge of the world are thus mutuallyindependent. (213)Knowledge of the contents of our own minds must, in most cases, be trivial. Thereason is that, apart from special cases, the problem of interpretation cannot arise.When I am asked about the propositional contents of my own mind, I must usemy own sentences. (213)“The second person”What’s the least n such that there could be n speakers of a language? Answer: 2.speaking a language…does not depend on two or more speakers speaking in thesame way; it merely requires that each speaker intentionally make himselfinterpretable to the other (the speaker must ‘go on’ more or less as the otherexpects, or at least is equipped to interpret).This is certainly a necessary condition for successful communication. But why is it a condition that must be satisfied in order to speak a language at all?Why couldn’t someone go on in the same way—satisfy all the conditions forbeing interpretable—without actually being intepreted? (115)What explains the fact that it seems so natural to say that the child is responding to the table, as opposed to, say, the retinal image of the table, when it utters ‘table’?The child finds tables similar; we find tables similar; and we find the child’sresponses in the presence of tables similar. It now makes sense for us to call theresponses of the child responses to tables. Given these three patterns of responsewe can assign a location to the stimuli that elicit the child’s responses…It is thecommon cause of our response and the child’s response.If we consider a single creature by itself, its responses, no matter how complex,cannot show that it is reacting to, or thinking about, events a certain distance away rather than, say, on its skin. The solipsist’s world can be any size; which is tosay…it is not a world. (119)Again, the move is from the conditions under which we know/have evidence for p to the conditions under which p is true.“Epistemology externalized”There is a presumption that we are right about the contents of our own minds; soin the cases where we are right, we have knowledgeThe ‘so’ is questionableBut any particular item of such knowledge is logicallyindependent of our beliefsabout a world outsideThe point seems to be that if P is a proposition to the effect that I am insuch-and-such mental state, and Q is a proposition about a world outside,the P and Q are logically independent. Hence, on this view, mental states are neither object-involving (believing that Smith is bald, seeing Jones), nor factive (knowing that it’s sunny, seeing that the cat is on the mat).and so cannot supply a foundation for science and commonsense beliefs. This ishow skeptics, like Hume, reason, and I think they are right; knowledge of thecontents of our own minds cannot be the basis for the rest of our knowledge. Here the ‘so’ seems quite unwarrranted (unless skepticism about induction is assumed).Suppose I think I see a mouse disappear behind a chair. Clearly this belief couldbe mistaken. But would this belief be wrong if I did not truly believe that a mouse was a small four-footed mammal, or a chair an object made for sitting? Shouldn’t this be: “But would I have this belief if I did not…”?Because of the holistic character of empirical belief, then, it is impossible that all our beliefs about the world are falseMore strongly:in the simplest case words and thoughts refer to what causes them…it cannothappen most of our plainest beliefs about what exists in the world are falseThe word/thought cases should be distinguished, since words (unlike, perhaps, thoughts) can be identified non-semantically.Davidson’s externalism distinguished from Putnam’s and Burge’s:I agree…that the usual cause of my use of the word determines what it means, Ido not see why sameness of microstructure is necessarily the relevant similarity.I am not impressed with the arguments for social externalism, for three reasons:1. [we understand a speaker best when we interpret him as he intended to beinterpreted; this will explain his actions far better than if we suppose he meansand thinks what someone else might mean and think who used the same words‘correctly’]2. [there is a conflict…with first person authority]Not clear why there is, given Davidson’s argument that Putnam-cases don’t pose a problem.3. [a general distrust of thought experiments that pretend to reveal what we wouldsay under conditions that in fact never arise]Hmm. What about the omniscient interpreter, swampman,…?Burge and I are essentially in agreement…on perceptual externalismAnyone who accepts perceptual externalism knows he cannot be systematicallydeceived about whether there are such things as cows, people, water, stars, andchewing gum.The argument of “the second person” again:The identification of the objects of thought rests, then, on a social basis。
MIT-SCIENCE-Lectures-03_e_identity_II
Difficult words encountered in reading:CadreMadrassahEthnonym: name of an ethnos/ethnic groupShi’i and SunniSufismAcculturationEthnogenesisPogromHegemonic3 ETHNIC IDENTITY IIFeb. 12, 2003Read: Gladney 25-5419-33Nagel:I. Ethnicity: what is it and how do we analyze it?A. Review: We’ve established that:seen in terms of relationshipbest1. Ethnicityis2. Ethnicity has to do with classification of groups of humansB. Today we’ll consider ethnicity seen as a process1. Nagel especially: introduces lots of terms relating to seeing ethnicity inthis wayC.The benefits of this approach:1. History is brought back in2. Change is allowed in the analysis3. People aren’t seen as objects—as “Xs” throughout timeis about classifications of humans, but there’s a lot more a. Ethnicityto it than thatII. Two perspectives can be taken:A. Analyze the position of an individual3 Ethnic Identity II OCW 3/22/041. Nagel’s point that ethnic identity lies at the intersection of individualethnic self-definition (who I am) and collective ethnic attribution (whothey say I am)identification and external ascription.internala. AdialecticbetweenB. Second perspective involves analyzing the group as a whole—from its point ofview1. Ethnic identity lies at the intersection of ethnic group self-definition (whowe are) and non-group ethnic attribution (who they say we are)2. Notice the different thrusts of the 2 authorsa. Nagel’s perspective is more individualistic than Gladney’sIII. What’s interesting about the Hui is that the state doesn’t use its own criteria when classifying the Hui into a single ethnic groupA. Why are the Hui so difficult to define as an ethnic group? Gladney shows thatthis is due to state policies1. The state created, invented the category (came up with a legal definition ofwho and who is not a member)2. Then lumped all Muslims not belonging to the 10 recognized Muslimnationalities into one “nationality”3. “Hui” became basically a default term for groups of Muslims who do nothave a language of their ownB. So in a sense we need a third perspective1. One that analyzes the state itselfformulations of ethnic policiesits2. Andinvestigatesa. And then analyzes why it doesn’t subscribe to them in certaincasescompletely rational, coherent, internallyneverb. Bureaucraciesarelogical; they have histories, cultures, power dynamicsIV. Approaches to analyzing ethnic processesA. One is to answer the question we asked last time: why ethnic resurgence?1. Mid-century US everyone saw ethnicity as incompatible with modernity2. Both the political right (who subscribed to assimilationist models) and left(who employed class models) predicted its disappearancea. The Right saw ethnic groups as eventually joining the mainstreamsociety—in US, Canada, Europepotideamelting1) Theb. The Left saw class solidarity eventually replacing ethnicidentification and loyalties3. We can’t rely on an evolutionary perspective for our analysisa. One that sees ethnic groups to be from a pre-modern timeb. That sees ethnicity to be a kind of vestigial feature characteristic ofmore traditional societies4. Nor can we analyze ethnicity as something biological, a feature ofancestry and genetics5. Such an analysis won’t explain the Hui, the Han, not, even, NativeAmerican peoplesB. The Adaptation Approach1. Sees ethnic change as processes of adaptation2. The Hui provide examplesChineselanguage (e.g., Gladney’s discussion ofthea. Adaptetymology of the 2 Chinese terms for “pure” and “truth”)b. Adapt their Islamic beliefs and practices to Confucianism, includeBuddhist architectural features in their mosquesC. Third approach: ethnicity seen as performance1. Language serving as emblem, permitting enactmentsa. The Hui’s use of the terms “pure and true”1) These words help the Hui perform their identity2) They are emblems that communicate to insiders andoutsiders alikeHuimarket men recognizing one another byexampleofb. Gladney’slistening to their speechPersian numbers to decide amongorArabic1) Usingthemselves what the price will be, then announcing it toHan buyers2. Ritual behavior, a kind of language that serves as emblems and enactsritualbathingrestrictions;a. Dietaryb. Gladney’s example of the man who refused to drink from a cup, itmight have been contaminated by a pork eaterc. This man was a self-avowed atheist, although he went to MosqueD. Fourth: ethnicity as dialectic1. Gladney’s point that after 30 years of being seen by the state simply asHui,diversity and multicultural background,linguistica. Despiteb. Now the Bai, Tibetan, Hainanese Muslims, Cantonese,Shanghainese, Fujianese non-Mandarin speakers themselves claimmembership to the same Hui ethnic group as other Hui in Chinathe birth of, origin of, a new form ofethnogenesis:isc. Thiscalledethnic identity1) Priorstaterecognition, the Hui recognized one anothertoas fellow Muslimsminzu (nationality)as2) Butnot3) Earlier, their ethnic consciousness was localized4) All Hui were brought closer together5) Through dialogue with state policy and local traditions6) “Pan-Hui” interaction and mandatory Hui schools2. Gladney’s point about the Han looking down on Hui as dirty, immorala. And the Hui looking down on Han because the Hui see themselvesas more pure and trueb. We have a dialecticc. The same thing happens with Gypsies, also known as Roma (self-name), who are often considered dirty by mainstream society, butwho consider themselves purer and cleaner than non-gypsiesE. Ethnicity seen as choice1. Nagel’s discussion of multilayered ethnicitya. This analytic perspective counteracts the “thingness” of mostnotions of ethnic groupsb. This “thingness” dissolves the closer we getc. An Indian. A Jew. A Chinese person, Latinos,Hispanics…African Americans…Asians…2. Nagel’s notion of ethnic choice refers to an individual choosing to keep ordiscard an ethnicitya. This feature, operating over time, explains the varying rates ofofficial membership for American Indians3. She makes a distinction between rational choice and nonrational choicea. I don’t care for this characterizationb. It sets up an either/or, and ranked opposition, but such choices areoften a little of both 1c. “Nonrational” is a put-down kind of word1) Implies that “rational” is a good strategy, understandable,the correct choice because it serves the individual’sinterests 1 See Sonia Alvarez, Evelina Dagnino, Arturo Escobar, 1998. Introduction: The cultural and the political in Latin American social movements. In Alvarez, Dagnino and Escobar, eds., Cultures of politics, politics of Cultures: Re-visioning Latin American social movements . Boulder: Westview: 1-32.otherreasons—a) Whereastodue“nonrational”isemotion influencing the choice, for example2) This terminology comes from a subfield of political sciencecalled Rational Choice Theory4. But it’s clear what she means by rational: a perceived advantage in theform of some kind of material or power gaina. As opposed to. some other kind of motive having to do withsymbolic meaning, feelings, sociability, recreational, etc.multiculturalismso popular today stems from symbolicoftheb. Lotsethnicity: fairs, taking classes in Celtic language, etc.5. And the notion of instrumentalist motives itself is usefula. It explains some of the movement by people into and out of ethniccategories6.There are many examples of choices being contesteda. Example: “Women are more Indian”1) The statement might be seen by men as a put down, achallengeb. University committees deciding which minorities areunderrepresented—it happens hereF. Ethnicity as non-choice: ascribed1. Back to the state: its interestsa. Examples: census, internment, immigration policy, determiningpolitical access and eligibility2. External limits on choice—imposed by society, the state, religiousinstitutionsareexampleanHuia. TheAmericansb. Africanghettoesc. Ethnicd. Ethnic cleansing (deportation, forced displacement)e. Killing, pogromse. Required markers1) Yellow star of David2) Stamping an identity card3. Internal limits on choicea. Don’t be a traitor, a sell-out, a “self-hating Jew”b. Such pressures can be strong, and can put someone in danger intimes of great conflict。
MIT-SCIENCE-Lectures-isometry03
Let ρ be a rotation. By Theorem 1, ρ is an orthogonal linear operator. Its determinant is ±1. The determinant varies continuously with the angle of rotation θ, and it is +1 when the angle is zero. Therefore it is +1 for all θ. Conversely, let p be an orthogonal linear operator with determinant 1. By Lemma 3, there is an eigenvector v1 such that pv1 = v1 . We choose a nonzero vector v2 orthogonal to v1 . Because the operator is orthogonal, pv2 is orthogonal to pv1 = v1 , and it has the same length as v2 . So v2 and pv2 are vectors of equal length in the plane orthogonal to v1 . There is a rotation ρ about the axis v1 which carries v2 to pv2 . Then ρ−1 p fixes both v1 and v2 . Moreover, being a composition of orthogonal operators with determinant 1, ρ−1 p is also an orthogonal � operator with determinant 1. By Lemma 4, ρ−1 p is the identity, and p = ρ.
MIT-SCIENCE-Lectures-pset2 (2)
Department of Urban Studies and Planning11.203 – MicroeconomicsFall, 2003Problem Set # 2Answers Due in your TA’s Box on Lecture 6This week’s problems continue applications of supply and demand and elasticity and begin discussion of utility maximization.1. In the U.S., the minimum wage is currently $5.15 per hour. Suppose that 13 millionworkers are paid at this level and the wage elasticity of labor demand for their services is -.4.a) Suppose the government passes legislation raising the minimum wage to $5.50per hour. Carefully explain what will happen to the total number of persons employed and the total amount of money going to minimum wage workers.Illustrate your answer with a diagram.b) As we said in class, an unemployed person is someone who wants to work atthe going market wage, but who cannot find work. Using this definition, calculate the increase in unemployed persons caused by the minimum wage rise. If you need more information to answer the question, carefully explain what additional information you need. Illustrate your answer with diagrams.c) You are part of a community organization in San Antonio, Texas organizing aliving wage campaign in which you use negotiation, political pressure and publicity to get employers to raise the base wage they pay. There are two candidates for the first firm you contact – a large hotel or an equally large firm doing light assembly of electronics components. Using the concept of elasticity, describe which one you choose.2. As we saw in lecture 4, we can begin to examine the incidence of a unit tax – say,$.25 per apple - by drawing two, parallel demand curves. At every quantity, the two demand curves are separated by a vertical distance of $.25 – the amount of the tax.The higher demand curve is the standard demand curve that consumers see (since their payment includes the tax). The lower demand curve is the curve producers now see and respond to – it represents the price the consumer pays minus the $.25 that goes to the tax. Satisfy yourself that the new equilibrium meets the following conditions:-The equilibrium quantity produced occurs at the point where the lower demand curve intersects with the supply curve (i.e. producers areresponding to the tax-reduced price they receive).-Consumers purchase this same equilibrium produced but the price they pay comes from the higher demand curve – i.e. they pay $.25 more perapple (the tax) than producers receive.-The price paid by consumers will increase by some amount – call it X.The price received by producers will fall by –Y (Y is a positivenumber and the price falls by minus that amount). The sum of X + Y= $ .25. The incidence of the tax refers to the way in which the $.25 issplit between the increase to consumers and the fall to producers.a) Draw two examples of the $.25 cent tax being imposed. In the first case, draw thedemand curve very elastic and the supply curve very inelastic. Describe how the tax is being divided between consumer and producer. In the second case, make draw the demand curve very inelastic and the supply curve very elastic. In this case, how is the tax divided between consumer and producer?b) Write in words a rough rule that describes the relationship between demandelasticity, supply elasticity and the incidence of a tax.3) Nicholson, p137, problem 4.7. (To do this problem, you need to understand the concepts of income elasticity and cross-price elasticity of demand. Both of these are discussed in Chapter 4.)4) Anti-AIDs drugs must typically be administered on a rigorous schedule. Failure to observe the schedule will make the drugs ineffective. This means that a country trying to deal with AIDS must carefully consider how to allocate its health budget between money spent on the drugs themselves and money spent on public health infrastructure (e.g. nurses who visit patients to see that drugs are taken on schedule).Define the goal as stabilized AIDs cases and assume the following principles apply: - A government must spend funds on both drugs and nurses to stabilize AIDS cases. Spending money on either alone will produce no results.-If we hold spending on drugs at a constant level, additional spending on nurses will stabilize more cases but each additional nurse will havea smaller impact than the previous nurse. Spending on drugs, holdingspending on nurses constant, shows a similar pattern.Below are four mathematical functions that describe the relationship between drugs, nurses and the number of stabilized cases. Use first derivatives, common sense, and graphs, if appropriate to explain why each function does or does not represent the problem as stated above. (The relevant first derivative formulae are contained in the calculus notes on the web page.)i) # Stabilized Cases = 10*(doses of drugs)2 + 5*(hours of nurses)2ii) # Stabilized Cases = 10*(doses of drugs) + 5*(hours of nurses)iii) # Stabilized Cases = 10*(doses of drugs)1/2 + 5*(hours of nurses)1/2 iv) # Stabilized Cases = 50*((doses of drugs)1/2 )* ((hours of nurses)1/2) where * = the multiplication sign and the exponent ½ = a square root*************************************************************。
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Traditions in American Concert Dance:Gender and Autobiography21M.670 SP.472Spring 2003 HASS-DGeneral Course Description:This course explores the forms, contents, and contexts of world traditions in dance that played a crucial role in shaping American concert dance. For example, we will identify dances from an African American vernacular tradition that were transferred from the social space to the concert stage. We will explore the artistic lives of such American dance artists as Katherine Dunham, and Alvin Ailey along with Isadora Duncan, Martha Graham, George Balanchine, and Merce Cunningham as American dance innovators. Of particular importance to our investigation will be the construction of gender and autobiography which lie at the heart of concert dance practice, and the ways in which these qualities have been choreographed by American artists. In the introductory arc of the class, we will ferret out the roots of classical ballet and its American presence via visiting ballerinas such as Fanny Essler and Marie Taglioni. From this we will trace a rise in performance venues; the Puritan resistance to dance as 'immoral;' and the breaking of tradition which allowed Isadora Duncan, Loie Fuller, and Ruth St. Denis to create a space for concert dance which was not ballet. We will uncover the streak of feminist independence which is at the root of modern dance practice. Martha Graham, Katherine Dunham, Pearl Primus, and Agnes de Mille fit directly into this lineage as first-generation modern dance artists. Class lectures and discussions will analyze works created by these artists, taking into consideration a variety of historical and political contexts which gave rise to their inventions. Frequent viewing assignments will help students identify visual, musical, and kinesthetic underpinnings of choreographic structure.The requirements for this subject conform to the mechanical requirements for all HASS-D's: There will be no fewer than three writing assignments that will add up to a minimum of 20 pages; there will be a final exam which will be scheduled by the Registrar's Office and which will account for a substantial portion of the grade (no less than 15%); and no less than one hour per week will be devoted to discussion.Readings and MaterialsCore TextsDancing by Gerald Jonas (New York: Harry Abrams, 1992).Modern Bodies: Dance and American Modernism from Martha Graham to Alvin Ailey by Julia L. Foulkes. Chapel Hill: University of North Carolina Press,2002.21M.670/SP.472 - Traditions in American Concert DanceSpring 2003Page 2.Tickets to two concert dance performances, to be determined.Class Requirements:1. Approximately 50 pages of reading and 1 hour of viewing weekly. Participationin class discussions will account for 10% of the final grade.2. We will attend at least two performances of dance concerts in the Boston area.3. Three short papers, of 7-10 pages length, on the topics described below inresponse to a video viewing of American concert work to be determined by theinstructor. All viewing assignments will be available at the Music Library, somewill be available in our private course locker. Short papers account for 45% ofthe final grade (15% each):Paper One - Religion and Social Order.Paper Two - Cultural Mores and Cultural IdentityPaper Three - Cultural Fusion4. A midterm oral project web-research assignment, defining a work of Americanconcert dance as classical art. The midterm assignment will account for 20% ofthe final grade.5. A final exam, in which students will be asked to synthesize material coveredthroughout the semester. The final exam will account for 25% of the final grade. Course Organization:The course will be divided into eight major units, as follows:UNIT I Introduction and Overview - 2 SessionsSession #1, #2What is tradition? And how do we identify traditions in American dance? A sharing of family traditions and viewing of contemporary American dance including music videos and concert dances. How do traditional dance forms construct gender? How is dance from different cultures typically presented the broadest American audience? What do these presentations tell us about the culture that produced the dance? This unit will provide students with a general overview of basic concepts such as dance, performance, kinesthesia, musicality, and culture.read "What is Art" by Betty Redfern in Routledge Dance Studies Reader pp 125-134 "The Power of Dance" in Dancing pp 12-35"Manifestos" Modern Bodies 8-26view Dancing: The Power of Dance21M.670/SP.472 - Traditions in American Concert DanceSpring 2003Page 3.Lecture Demonstration/Master Class: Rennie Harris PureMovement at Killian Hall Friday,One Day After Session #2 at 4pm.Members of Rennie Harris' Puremovement Dance Company,masters of hip-hop. popping, locking, stepping. break, house andother styles from inner city America will present a lecture on theartform, followed by a dance class.UNIT II Dance as an expression of religious worship - 3 SessionsSession #3, #4, #5How has American concert dance been inspired by religious dances of the world? A focus on Indian dance forms, with a consideration of Ruth St. Denis' Westernized "Indian" dances. Howdo these dances conflate gender and spirituality?read "Lord of the Dance" in Dancing pp 36-69"Christian Conversion and the Challenge of Dance" by P. Sterling Stuckey(Dancing Many Drums, DeFrantz, ed., U Wisconsin Press, 2002)view Dancing "Lord of the Dance"Revelations by Alvin AileyPaper #1 Due in Session #5 - How does the dance "Revelations" (Ailey, 1960) convey concepts of religion and social order?UNIT III Dance as an expression of social order and power - 3 SessionsSession #6, #7, #8How can concert dance express social order? A focus on the court roots of ballet; introductionto the Bennington school; and a consideration of Doris Humphrey's "With My Red Fires."read "Dance of the Realm" in Dancing pp 70-107"Pioneer Women" in Modern Bodies pp 27-50"An Introduction to Choreography" from The Art of Making Dances by DorisHumphrey, Grove Press, New York, pp. 15-41view Dancing "Dance of the Realm"Doris Humphrey, "New Dance"Special Event in Session #8: Jigna Desia, Mit Alum, will give an invited lecture titled “Watching "Home" Movies: Hollywood Cinema in South Asian America.”UNIT IV Dance as an expression of cultural mores - 3 SessionsSession #9, #10, #1121M.670/SP.472 - Traditions in American Concert DanceSpring 2003Page 4.How does concert dance confirm gender expectations? A focus on gender-specific behaviorand dance in the Middle East, with an examination of Ted Shawn’s all-male dance ensemble.Also, a look at British choreographer Lloyd Newsom’s DV8 physical theater.read "Social Dance" in Dancing pp 108-127"Men Must Dance" in Modern Bodies pp 79-103"Simmering Passivity: The Black Male Body in Concert Dance" by ThomasDeFrantz, in Moving Ideologies, Gay Morris, ed., Routledge, 1996, 106-121."Dancing in the Dark: Rationalism and the Neglect of Social Dance" by AndrewH. Ward in Dance, Sex, and Gender, Helen Thomas, ed., St. Martin's Press,1993, 16-33.view Dancing "Sex and Social Dance"Ted Shawn "Kinetic Molpai"Bill T. Jones "Fever Swamp"Paper #2 Due Two Days After Session #11 - How does the dance "Fall River Legend" (DeMille, 1950) convey concepts of Cultural Mores and Cultural Identity?Performance Event between Sessions #10 and #11: Mark Morris Group at the Shubert Theater UNIT V Dance as an emblem of cultural identity - 2 SessionsSession #12, #13How does concert dance confirm identity for minority populations? A focus on African danceforms in diaspora, with an examination of popular dance forms from the United States. AreAfrican dance forms always configured with male drummers and female dancers?read "New Worlds of Dance" in Dancing, pp 164-189"Primitive Moderns" in Modern Bodies, 51-78Malone, Jacqui "'Keep to the Rhythm and You'll Keep To Life': Meaning andStyle in African American Vernacular Dance" in Routledge Dance StudiesReader pp 230-235Nash, Joe "The Mission of Black Modern Dance" American Dance FestivalMyers, Gerald " African Americans and the Modern Dance Aesthetic" AmericanDance FestivalThompson, Robert Farris "Dance and Culture, An Aesthetic of the Cool: WestAfrica Dance" in African Forum 2, no. 2; Fall 1996: pp 85-102view Dance Black America (1983)21M.670/SP.472 - Traditions in American Concert DanceSpring 2003Page 5.Special Lecture Seven Days After Session #15: Yutian Wong, Professor at Bryn Mar College, will deliver invited lecture “Upstaging Orientalism: Performing Race and Gender in (Asian) AmericanModern/Postmodern Dance.”UNIT VI Dance as a classical art - 4 SessionsSession #14, #15, #16, #17How does concert dance function as a classical art? What is classicism? Is ballet inherentlymisogynistic? A focus on kabuki in Japan and ballet in America, with a consideration of thechoreography of George Balanchine, Jerome Robbins, and Lar Lubovitch.read "Classical Dance Theater" in Dancing pp 128-163"Organizing Dance" in Modern Bodies pp 104-129Kealiinohomoku, Joann "An Anthropologist Looks at Ballet as a Form of EthnicDance" in Cohen & Copeland, What Is Dance?, Oxford: OxfordUniversity Press 1983: 533-549Novak, Cynthia "Ballet, Gender and Cultural Politics" in Dance, Gender andCulture, Helen Thomas, ed., New York: St. Martin's Press, 1993Daly, Ann "The Balanchine Woman: Of Hummingbirds and Channel Swimmers"in TDR Vol 31 NO. 1, 1987view George Balanchine Agon, Jewels, Prodigal SonDancing "Classical Dance Theater"In Class Presentations Begin Two Days After Session #16UNIT VII Dance as a medium of Cultural Fusion - 1 SessionSession #18How can concert dance fuse culture together? A focus on dances in the Americas, with aconsideration of Martha Graham's theatrical transformations of Native American rituals, andKatherine Dunham's adaptation of Santeria ritual.read Huenemann, Lynn "Northern Plains Dance" in Native American Dance:Ceremonies and Social Traditions edited by Charlotte Heth, SmithsonianInstitution/Starwood, 1993, pp. 125-147"Dancing America" in Modern Bodies pp 130-156Dixon Gottschild, Brenda "Barefoot and Hot, Sneakered and Cool: AfricanistSubtexts in Modern and Postmodern Dance" in Digging the AfricanistPresence: Dance and Other Contexts Greenwood, 1996: pp 47-58view Dancing "Dancing on One World"Performance Event between Sessions #16 and #17: Alvin Ailey American Dance Theater at the Wang CeUNIT VIII Dance as the autobiographical creation of individual artists - 2 Sessions Session #19, #20How can concert dance be an intimate, personal expression? A focus on contemporary dance in the United States, with an examination of the work of Yvonne Rainer, Twyla Tharp, andMerce Cunningham.read "Modernizing Dance" in Dancing pp 190-237Jowitt, Deborah "A Private View of Dance Criticism" The Dance Has ManyFaces, Walter Sorell, ed., Third Revised Edition, 1992: 202-209Graham, Martha "I Am a Dancer" in Routledge Dance Studies Reader pp 66-71Dempster, Elizabeth "Women Writing The Body: Let's Watch a Little How SheDances" in Routledge Dance Studies Reader pp 223-229Brown, Carol "Re-tracing our steps: The Possibilities for Feminist DanceHistories" in Dance History: An Introduction edited by Janet Adshead-Lansdale and June Layson, Routledge, 1983, 198-216 view Dancing "Individual and Tradition"Yvonne Rainer "Trio A" (1966)Twyla Tharp Catherine WheelMerce Cunningham StoryPaper #3 Due Session #19 - How does the "gold section" of The Catherine Wheel(Tharp, 1981) describe issues of gender and individuality?Wrap up and Review - 1 Session - Session #21。